Mathematical models of host plant infection by helper-dependent virus complexes: Why are helper viruses always avirulent?

Interactions between viruses in plants are common, and some viruses depend on such interactions for their survival. Frequently, a virus lacks some ess ential molecular function that another provides. In "helper-dependent" viru s complexes, the helper virus is transmitted independently by a vector, whe reas the dependent virus depends on molecular agents associated with the he lper virus for transmission by a vector. A general mathematical model was d eveloped of the dynamics of host plant infection by a helper-dependent viru s complex. Four categories of host plants were considered: healthy, infecte d with helper virus alone, infected with dependent virus alone, and infecte d with both viruses. New planting of the host crop was constrained by a max imum abundance due to limitation of the cropping area. The ratio of infecti on rate to host loss rate due infection is proposed as an important epidemi ological quantity, A, that can be used as a measure of the mutual adaptatio n of the virus and host. A number of alternative equilibria of host infecti on could occur and were determined exclusively by parameter values; it was informative to display their distribution in the parameter plane: (1/A)(hel per) versus (1/A)(dependent). A simple analysis of the distribution of the final equilibria illustrated that the dependent virus could affect the surv ival of the helper virus, so facilitation between the two can be reciprocal . The distribution of the final equilibria also indicated that a well-adapt ed helper virus increases the opportunity for a dependent virus to evolve a nd survive, and the model, therefore, explains why infection with a helper virus usually causes no or little damage to plants, whereas infection with a dependent virus or mixed infection with both often causes very severe dam age.